Question: Solve for $x$ and $y$ using elimination. ${x+6y = 20}$ ${-x+5y = 2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $11y = 22$ $\dfrac{11y}{{11}} = \dfrac{22}{{11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x+6y = 20}\thinspace$ to find $x$ ${x + 6}{(2)}{= 20}$ $x+12 = 20$ $x+12{-12} = 20{-12}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {-x+5y = 2}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(2)}{= 2}$ ${x = 8}$